The ‘moving walkway’ is a 300-foot long conveyor belt that

[neeshpal]

The "˜moving walkway’ is a 300-foot long conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a combined rate (including both walkway and foot speed) of 6 feet per second, reaches the group of people, and then remains stationary until the walkway ends. What is Bill’s average rate of movement for his trip along the moving walkway?


Can someone help me get the correct answer. I am not sure of answer because someone has posted this in a forum.

[StaceyKoprince]

Hey, Neeshpal - for copyright reasons, we always require that the source of a question (the author, not just the forum on which you found it) be posted. You're lucky, though, because I recognize this question - it's one of ours. :)

I'm not sure if you just want to know what the answer is to check or if you want the explanation. Just in case, I'll only tell you the answer choices and correct answer now (so you can try it yourself first). Post again if you want an explanation.

The answer choices are 2 ft/s, 2.5, 3, 4 and 5.

The right answer is E.

[unique]

MGMAT staff - let me know if this is correct

Bill have to cover 300F
He walks towards the ppl in 120/6 = 20 sec
In20 sec the walkway has advanced by 20*3 = 60F

So now Bill has to cover 300 - (120+60) = 120 F
time taken for that 120/3 = 40 sec

avg = 300/60 = 5

[StaceyKoprince]

Not quite, though you got lucky!

Bill is 120 feet from the group. The group is moving at 3fps and Bill is moving at 6fps, so he's gaining on them at 3fps. Therefore it takes him 120/3 = 40sec to catch up to them. In 40 sec, the group moves another 120 feet, so Bill catches up at the 240-foot mark. It then takes 60/3 = 20 sec to go the final 60 feet. 300feet / 60sec = 5fps.

[josephgreer]

I got this problem correct on the sample test, however, I burned quite some time due to the following perceived ambiguity.

The problem states not that the "walkway" is 300 feet long, rather it states the "belt" is 300 feet long. Since a conveyor belt walkway is usually 1/2 the length of the conveyor belt, I assumed the length of the walkway was approximately 150 feet long.

Since the people standing on the belt are 120 feet away when Bill steps on the belt, they will reach the end of the belt in 10 seconds (30 feet to go to get to 150 feet and moving at a rate of 3-feet/second).

Only after burning about 45 seconds in calculation time, did I recognize that given my 150-foot length assumption the people would be reaching the end of the walkway before Bill had reached them. Since I didn't know the rate at which they would walk after leaving the belt, I knew the writer meant that the conveyor walkway (not the conveyor belt). From there, I had to start over.

Was I the only one who approached the problem this way? Also, is this ambiguity something that can be expected on the GMAT? In other words, is it in a way a data sufficiency problem?

[RonPurewal]

That's some awfully astute reading; I bet you're smashingly good at critical reasoning. :)

I'll make sure someone looks at this.

[christiancryan]

Our fault -- we meant that the walkway was 300 feet long. I've adjusted the question to reflect that meaning unambiguously. Thanks for the flag, Joseph!

[StaceyKoprince]

Yes, I agree - nice catch! It is possible (but not likely) to see something like this as an experimental question on the official GMAT b/c a question writer might overlook the distinction (as this question writer apparently did). However, official GMAT questions have to make it through that experimental phase before they can graduate to full-fledged questions that count towards a tester's score. If enough people thought as you did, that would push up the average time spent on the question and the test writers would have to investigate - either find the problem and fix it, or drop the question entirely. Essentially, the real test has a built-in mechanism to catch potential issues with problem before the questions go "live."

(Oh - and I said it was possible but not likely b/c things like this rarely slip through the cracks, for them or for us. It's such a specific little thing - this just isn't going to happen to occur very much. At the same time, I typically find at least one thing on any given test with which I want to argue. But maybe that's just because I enjoy arguing. ;)

[DCE]

Please let me know if I am doing something wrong here

Lets divide the distance on belt i.e 300 feets into two halfs - one in Bill walks at 6 and the other in which Bill walks at 3.

So for the first part Bill walks at 6 only till the time he has to do the catching to the group ie 120 feet

Time for this case is = 120/6 = 20 secs.
In this time the belt is moving so even it covers a distance of 20*3 = 60 feet

Now the remaining 300 - 120 - 60 = 120 feet left.

For this 120 feet only the belt moves, therefore the time = 120/3 = 40 secs

Total time is 60 secs and we get the speed as 300/60 = 5

Thanks,
DCE

[RonPurewal]

Please let me know if I am doing something wrong here

Lets divide the distance on belt i.e 300 feets into two halfs - one in Bill walks at 6 and the other in which Bill walks at 3.

So for the first part Bill walks at 6 only till the time he has to do the catching to the group ie 120 feet

Time for this case is = 120/6 = 20 secs.
In this time the belt is moving so even it covers a distance of 20*3 = 60 feet

Now the remaining 300 - 120 - 60 = 120 feet left.

For this 120 feet only the belt moves, therefore the time = 120/3 = 40 secs

Total time is 60 secs and we get the speed as 300/60 = 5

Thanks,
DCE

your solution is the same as that posted by 'unique' (see above).
therefore, stacey's critique of that solution applies to yours as well.

[pujaverma]

What I don't understand is that if the group has moved an additional 120 feet in 40 seconds, would it not take Bill 80 seconds to catch up to them at the 240 foot mark? 40 seconds for the first 120 feet and 40 seconds for the next 120 feet.

[misrapreeti1]

I agree with Puja Verma(pujaverma). What about the additional time taken by Bill to catch up the team who had moved 120 feet within that 40 secs?

[RonPurewal]

What I don't understand is that if the group has moved an additional 120 feet in 40 seconds, would it not take Bill 80 seconds to catch up to them at the 240 foot mark? 40 seconds for the first 120 feet and 40 seconds for the next 120 feet.

here's the deal:
the group is just standing on the walkway. they are not moving.
so:
the GROUP is moving at 3 ft/sec, AS MEASURED ALONG THE GROUND
the GROUP is moving at 0 ft/sec, AS MEASURED ACCORDING TO THE WALKWAY.

bill is walking at a COMBINED rate of 6 ft/sec, MEASURED ALONG THE GROUND. since the walkway itself is moving at 3 ft/sec, this means that bill is moving at 6 - 3 = 3 ft/sec ALONG THE WALKWAY.
so:

in 40 seconds,
the GROUP has moved 0 feet ALONG THE WALKWAY, and bill has moved 120 feet ALONG THE WALKWAY. thus bill has caught up to the group.

in that same 40 seconds,
the GROUP has moved 120 feet MEASURED ALONG THE GROUND, and bill has moved 240 feet MEASURED ALONG THE GROUND.

therefore, there is no "additional" 120 feet to travel; all they have to do is wait out the final 60 feet.